LMFDB - Embedded newform 126.9.s.a.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(53,126)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("126.53");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 5826111 x^{18} - 52434714 x^{17} + 14609902138197 x^{16} - 116878028586684 x^{15} + \cdots + 46\!\cdots\!67 $ x^20 - 10x^19 + 5826111x^18 - 52434714x^17 + 14609902138197x^16 - 116878028586684x^15 + 20570415019216091666x^14 - 143990859773172188876x^13 + 17778850839861393261577389x^12 - 106671233163309243180965870x^11 + 9680290789684647638481756224861x^10 - 48400476132217676087684309052126x^9 + 3275735646651808421941058995933509711x^8 - 13102652184923818063474053937427650164x^7 + 653502209053902071586784989674537854288110x^6 - 1960460768082339807775059434296031383524340x^5 + 68850375563113059318225998877994832003827914811x^4 - 137697483706898978818817917958243091010522758690x^3 + 3066443413106133675142280126674379287603657139937675x^2 - 3066374564691021503239083252322344289284140820347058*x + 46867859601845955405133191126273914741044351570054374867
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{16}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.1
Root			$0.500000 + 962.962i$ of defining polynomial
Character	$\chi$	$=$	126.53
Dual form			126.9.s.a.107.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-834.700 + 481.914i) q^{5} +(-1891.88 + 1478.37i) q^{7} +1448.15i q^{8} +O(q^{10})$	\(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-834.700 + 481.914i) q^{5} +(-1891.88 + 1478.37i) q^{7} +1448.15i q^{8} +(5452.24 - 9443.55i) q^{10} +(15464.1 + 8928.20i) q^{11} +49919.6 q^{13} +(10173.7 - 25187.1i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(102719. + 59304.9i) q^{17} +(-76293.2 - 132144. i) q^{19} +123370. i q^{20} -202022. q^{22} +(4175.14 - 2410.52i) q^{23} +(269170. - 466216. i) q^{25} +(-489110. + 282388. i) q^{26} +(42798.4 + 304333. i) q^{28} +50212.6i q^{29} +(79829.4 - 138269. i) q^{31} +(160530. + 92681.9i) q^{32} -1.34192e6 q^{34} +(866709. - 2.14572e6i) q^{35} +(1.44056e6 + 2.49512e6i) q^{37} +(1.49503e6 + 863159. i) q^{38} +(-697886. - 1.20877e6i) q^{40} +4.02906e6i q^{41} +234158. q^{43} +(1.97940e6 - 1.14281e6i) q^{44} +(-27271.9 + 47236.3i) q^{46} +(-2.36482e6 + 1.36533e6i) q^{47} +(1.39365e6 - 5.59381e6i) q^{49} +6.09062e6i q^{50} +(3.19485e6 - 5.53365e6i) q^{52} +(9.68616e6 + 5.59231e6i) q^{53} -1.72105e7 q^{55} +(-2.14091e6 - 2.73974e6i) q^{56} +(-284045. - 491981. i) q^{58} +(1.62118e7 + 9.35988e6i) q^{59} +(-1.07165e7 - 1.85615e7i) q^{61} +1.80633e6i q^{62} -2.09715e6 q^{64} +(-4.16679e7 + 2.40569e7i) q^{65} +(-1.40946e7 + 2.44125e7i) q^{67} +(1.31480e7 - 7.59103e6i) q^{68} +(3.64604e6 + 2.59265e7i) q^{70} -1.46554e7i q^{71} +(-1.25100e7 + 2.16679e7i) q^{73} +(-2.82290e7 - 1.62980e7i) q^{74} -1.95311e7 q^{76} +(-4.24554e7 + 5.97051e6i) q^{77} +(-1.45422e7 - 2.51878e7i) q^{79} +(1.36757e7 + 7.89568e6i) q^{80} +(-2.27918e7 - 3.94766e7i) q^{82} +1.96403e7i q^{83} -1.14319e8 q^{85} +(-2.29427e6 + 1.32460e6i) q^{86} +(-1.29294e7 + 2.23944e7i) q^{88} +(-4.45431e7 + 2.57170e7i) q^{89} +(-9.44421e7 + 7.37995e7i) q^{91} -617092. i q^{92} +(1.54469e7 - 2.67548e7i) q^{94} +(1.27364e8 + 7.35335e7i) q^{95} +1.52770e8 q^{97} +(1.79884e7 + 6.26916e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) $ 20 * q + 1280 * q^4 - 3710 * q^7	$ 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) $ 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−9.79796	+	5.65685i	−0.612372	+	0.353553i
$2$	−9.79796	+	5.65685i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	64.0000	−	110.851i	0.250000	−	0.433013i
$5$	−834.700	+	481.914i	−1.33552	+	0.771063i	−0.986139	−	0.165919i	$-0.946941\pi$
$5$	−834.700	+	481.914i	−1.33552	+	0.771063i	−0.349380	+	0.936981i	$0.613608\pi$
$6$		0			0
$7$	−1891.88	+	1478.37i	−0.787957	+	0.615730i
$7$	−1891.88	+	1478.37i	−0.787957	+	0.615730i
$8$			1448.15i			0.353553i
$9$		0			0
$10$	5452.24	−	9443.55i	0.545224	−	0.944355i
$11$	15464.1	+	8928.20i	1.05622	+	0.609808i	0.924384	−	0.381464i	$-0.124580\pi$
$11$	15464.1	+	8928.20i	1.05622	+	0.609808i	0.131835	+	0.991272i	$0.457913\pi$
$12$		0			0
$13$	49919.6			1.74782			0.873912	−	0.486085i	$-0.161575\pi$
$13$	49919.6			1.74782			0.873912	+	0.486085i	$0.161575\pi$
$14$	10173.7	−	25187.1i	0.264830	−	0.655641i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	102719.	+	59304.9i	1.22986	+	0.710060i	0.967001	−	0.254774i	$-0.0820012\pi$
$17$	102719.	+	59304.9i	1.22986	+	0.710060i	0.262859	+	0.964834i	$0.415335\pi$
$18$		0			0
$19$	−76293.2	−	132144.i	−0.585425	−	1.01399i	−0.994822	−	0.101630i	$-0.967594\pi$
$19$	−76293.2	−	132144.i	−0.585425	−	1.01399i	0.409397	−	0.912356i	$-0.365739\pi$
$20$			123370.i			0.771063i
$21$		0			0
$22$	−202022.			−0.862399
$23$	4175.14	−	2410.52i	0.0149197	−	0.00861388i	−0.492522	−	0.870300i	$-0.663925\pi$
$23$	4175.14	−	2410.52i	0.0149197	−	0.00861388i	0.507441	+	0.861686i	$0.330591\pi$
$24$		0			0
$25$	269170.	−	466216.i	0.689075	−	1.19351i
$26$	−489110.	+	282388.i	−1.07032	+	0.617949i
$27$		0			0
$28$	42798.4	+	304333.i	0.0696298	+	0.495128i
$29$			50212.6i			0.0709938i	0.999370	+	0.0354969i	$0.0113014\pi$
$29$			50212.6i			0.0709938i	−0.999370	+	0.0354969i	$0.988699\pi$
$30$		0			0
$31$	79829.4	−	138269.i	0.0864402	−	0.149719i	−0.819564	−	0.572988i	$-0.805784\pi$
$31$	79829.4	−	138269.i	0.0864402	−	0.149719i	0.906004	+	0.423269i	$0.139118\pi$
$32$	160530.	+	92681.9i	0.153093	+	0.0883883i
$33$		0			0
$34$	−1.34192e6			−1.00418
$35$	866709.	−	2.14572e6i	0.577565	−	1.42988i
$36$		0			0
$37$	1.44056e6	+	2.49512e6i	0.768640	+	1.33132i	0.938300	+	0.345821i	$0.112400\pi$
$37$	1.44056e6	+	2.49512e6i	0.768640	+	1.33132i	−0.169660	+	0.985503i	$0.554267\pi$
$38$	1.49503e6	+	863159.i	0.716996	+	0.413958i
$39$		0			0
$40$	−697886.	−	1.20877e6i	−0.272612	−	0.472177i
$41$			4.02906e6i			1.42583i	0.701249	+	0.712916i	$0.252626\pi$
$41$			4.02906e6i			1.42583i	−0.701249	+	0.712916i	$0.747374\pi$
$42$		0			0
$43$	234158.			0.0684914			0.0342457	−	0.999413i	$-0.489097\pi$
$43$	234158.			0.0684914			0.0342457	+	0.999413i	$0.489097\pi$
$44$	1.97940e6	−	1.14281e6i	0.528109	−	0.304904i
$45$		0			0
$46$	−27271.9	+	47236.3i	−0.00609093	+	0.0105498i
$47$	−2.36482e6	+	1.36533e6i	−0.484625	+	0.279799i	−0.722342	−	0.691536i	$-0.756934\pi$
$47$	−2.36482e6	+	1.36533e6i	−0.484625	+	0.279799i	0.237717	+	0.971335i	$0.423601\pi$
$48$		0			0
$49$	1.39365e6	−	5.59381e6i	0.241752	−	0.970338i
$50$			6.09062e6i			0.974499i
$51$		0			0
$52$	3.19485e6	−	5.53365e6i	0.436956	−	0.756830i
$53$	9.68616e6	+	5.59231e6i	1.22758	+	0.708741i	0.966522	−	0.256583i	$-0.0825968\pi$
$53$	9.68616e6	+	5.59231e6i	1.22758	+	0.708741i	0.261054	+	0.965324i	$0.415930\pi$
$54$		0			0
$55$	−1.72105e7			−1.88080
$56$	−2.14091e6	−	2.73974e6i	−0.217694	−	0.278585i
$57$		0			0
$58$	−284045.	−	491981.i	−0.0251001	−	0.0434747i
$59$	1.62118e7	+	9.35988e6i	1.33790	+	0.772435i	0.986495	−	0.163790i	$-0.0523718\pi$
$59$	1.62118e7	+	9.35988e6i	1.33790	+	0.772435i	0.351402	+	0.936225i	$0.385705\pi$
$60$		0			0
$61$	−1.07165e7	−	1.85615e7i	−0.773986	−	1.34058i	−0.935363	−	0.353690i	$-0.884927\pi$
$61$	−1.07165e7	−	1.85615e7i	−0.773986	−	1.34058i	0.161377	−	0.986893i	$-0.448406\pi$
$62$			1.80633e6i			0.122245i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	−4.16679e7	+	2.40569e7i	−2.33425	+	1.34768i
$66$		0			0
$67$	−1.40946e7	+	2.44125e7i	−0.699443	+	1.21147i	0.269217	+	0.963079i	$0.413235\pi$
$67$	−1.40946e7	+	2.44125e7i	−0.699443	+	1.21147i	−0.968660	+	0.248391i	$0.920098\pi$
$68$	1.31480e7	−	7.59103e6i	0.614930	−	0.355030i
$69$		0			0
$70$	3.64604e6	+	2.59265e7i	0.151855	+	1.07982i
$71$		−	1.46554e7i		−	0.576719i	−0.957522	−	0.288360i	$-0.906890\pi$
$71$		−	1.46554e7i		−	0.576719i	0.957522	−	0.288360i	$-0.0931099\pi$
$72$		0			0
$73$	−1.25100e7	+	2.16679e7i	−0.440520	+	0.763003i	−0.997728	−	0.0673699i	$-0.978539\pi$
$73$	−1.25100e7	+	2.16679e7i	−0.440520	+	0.763003i	0.557208	+	0.830373i	$0.311873\pi$
$74$	−2.82290e7	−	1.62980e7i	−0.941388	−	0.543511i
$75$		0			0
$76$	−1.95311e7			−0.585425
$77$	−4.24554e7	+	5.97051e6i	−1.20773	+	0.169843i
$78$		0			0
$79$	−1.45422e7	−	2.51878e7i	−0.373354	−	0.646669i	0.616725	−	0.787179i	$-0.288459\pi$
$79$	−1.45422e7	−	2.51878e7i	−0.373354	−	0.646669i	−0.990079	+	0.140510i	$0.955126\pi$
$80$	1.36757e7	+	7.89568e6i	0.333880	+	0.192766i
$81$		0			0
$82$	−2.27918e7	−	3.94766e7i	−0.504108	−	0.873140i
$83$			1.96403e7i			0.413844i	0.978357	+	0.206922i	$0.0663446\pi$
$83$			1.96403e7i			0.413844i	−0.978357	+	0.206922i	$0.933655\pi$
$84$		0			0
$85$	−1.14319e8			−2.19000
$86$	−2.29427e6	+	1.32460e6i	−0.0419422	+	0.0242153i
$87$		0			0
$88$	−1.29294e7	+	2.23944e7i	−0.215600	+	0.373430i
$89$	−4.45431e7	+	2.57170e7i	−0.709938	+	0.409883i	−0.811038	−	0.584993i	$-0.801097\pi$
$89$	−4.45431e7	+	2.57170e7i	−0.709938	+	0.409883i	0.101100	+	0.994876i	$0.467764\pi$
$90$		0			0
$91$	−9.44421e7	+	7.37995e7i	−1.37721	+	1.07619i
$92$		−	617092.i		−	0.00861388i
$93$		0			0
$94$	1.54469e7	−	2.67548e7i	0.197847	−	0.342682i
$95$	1.27364e8	+	7.35335e7i	1.56369	+	0.902799i
$96$		0			0
$97$	1.52770e8			1.72564			0.862819	−	0.505512i	$-0.168697\pi$
$97$	1.52770e8			1.72564			0.862819	+	0.505512i	$0.168697\pi$
$98$	1.79884e7	+	6.26916e7i	0.195024	+	0.679681i
$99$		0			0
$100$	−3.44537e7	−	5.96756e7i	−0.344537	−	0.596756i
$101$	−6.21632e6	−	3.58899e6i	−0.0597376	−	0.0344895i	0.469834	−	0.882755i	$-0.344314\pi$
$101$	−6.21632e6	−	3.58899e6i	−0.0597376	−	0.0344895i	−0.529571	+	0.848265i	$0.677647\pi$
$102$		0			0
$103$	2.81537e7	+	4.87637e7i	0.250142	+	0.433259i	0.963565	−	0.267475i	$-0.0861893\pi$
$103$	2.81537e7	+	4.87637e7i	0.250142	+	0.433259i	−0.713423	+	0.700734i	$0.752856\pi$
$104$			7.22913e7i			0.617949i
$105$		0			0
$106$	−1.26539e8			−1.00231
$107$	−1.21737e8	+	7.02849e7i	−0.928726	+	0.536200i	−0.886409	−	0.462904i	$-0.846808\pi$
$107$	−1.21737e8	+	7.02849e7i	−0.928726	+	0.536200i	−0.0423179	+	0.999104i	$0.513474\pi$
$108$		0			0
$109$	6.04976e7	−	1.04785e8i	0.428580	−	0.742323i	−0.568167	−	0.822913i	$-0.692347\pi$
$109$	6.04976e7	−	1.04785e8i	0.428580	−	0.742323i	0.996747	+	0.0805904i	$0.0256806\pi$
$110$	1.68628e8	−	9.73573e7i	1.15175	−	0.664963i
$111$		0			0
$112$	3.64748e7	+	1.47331e7i	0.231804	+	0.0936314i
$113$		−	1.48817e8i		−	0.912725i	−0.889794	−	0.456362i	$-0.849152\pi$
$113$		−	1.48817e8i		−	0.912725i	0.889794	−	0.456362i	$-0.150848\pi$
$114$		0			0
$115$	−2.32332e6	+	4.02411e6i	−0.0132837	+	0.0230080i
$116$	5.56613e6	+	3.21361e6i	0.0307412	+	0.0177485i
$117$		0			0
$118$	−2.11790e8			−1.09239
$119$	−2.82007e8	+	3.96587e7i	−1.40628	+	0.197765i
$120$		0			0
$121$	5.22460e7	+	9.04927e7i	0.243731	+	0.422155i
$122$	2.09999e8	+	1.21243e8i	0.947935	+	0.547290i
$123$		0			0
$124$	−1.02182e7	−	1.76984e7i	−0.0432201	−	0.0748594i
$125$			1.42372e8i			0.583154i
$126$		0			0
$127$	−4.43458e8			−1.70466			−0.852330	−	0.523005i	$-0.824811\pi$
$127$	−4.43458e8			−1.70466			−0.852330	+	0.523005i	$0.824811\pi$
$128$	2.05478e7	−	1.18633e7i	0.0765466	−	0.0441942i
$129$		0			0
$130$	2.72173e8	−	4.71418e8i	0.952954	−	1.65057i
$131$	−2.47913e7	+	1.43133e7i	−0.0841811	+	0.0486020i	−0.541500	−	0.840701i	$-0.682143\pi$
$131$	−2.47913e7	+	1.43133e7i	−0.0841811	+	0.0486020i	0.457319	+	0.889303i	$0.348810\pi$
$132$		0			0
$133$	3.39695e8	+	1.37211e8i	1.08563	+	0.438513i
$134$		−	3.18923e8i		−	0.989161i
$135$		0			0
$136$	−8.58827e7	+	1.48753e8i	−0.251044	+	0.434821i
$137$	−2.46937e8	−	1.42569e8i	−0.700977	−	0.404709i	0.106735	−	0.994288i	$-0.465961\pi$
$137$	−2.46937e8	−	1.42569e8i	−0.700977	−	0.404709i	−0.807711	+	0.589579i	$0.799294\pi$
$138$		0			0
$139$	4.96625e8			1.33036			0.665180	−	0.746683i	$-0.268355\pi$
$139$	4.96625e8			1.33036			0.665180	+	0.746683i	$0.268355\pi$
$140$	−1.82386e8	−	2.33402e8i	−0.474767	−	0.607564i
$141$		0			0
$142$	8.29035e7	+	1.43593e8i	0.203901	+	0.353167i
$143$	7.71961e8	+	4.45692e8i	1.84608	+	1.06584i
$144$		0			0
$145$	−2.41981e7	−	4.19124e7i	−0.0547407	−	0.0948136i
$146$		−	2.83069e8i		−	0.622989i
$147$		0			0
$148$	3.68782e8			0.768640
$149$	−3.03090e8	+	1.74989e8i	−0.614930	+	0.355030i	−0.774893	−	0.632093i	$-0.782196\pi$
$149$	−3.03090e8	+	1.74989e8i	−0.614930	+	0.355030i	0.159962	+	0.987123i	$0.448863\pi$
$150$		0			0
$151$	−1.21967e8	+	2.11254e8i	−0.234604	+	0.406347i	−0.959158	−	0.282872i	$-0.908713\pi$
$151$	−1.21967e8	+	2.11254e8i	−0.234604	+	0.406347i	0.724553	+	0.689219i	$0.242046\pi$
$152$	1.91364e8	−	1.10484e8i	0.358498	−	0.206979i
$153$		0			0
$154$	3.82202e8	−	2.98663e8i	0.679533	−	0.531005i
$155$			1.53884e8i			0.266603i
$156$		0			0
$157$	2.76334e8	−	4.78624e8i	0.454815	−	0.787763i	−0.543862	−	0.839175i	$-0.683039\pi$
$157$	2.76334e8	−	4.78624e8i	0.454815	−	0.787763i	0.998678	+	0.0514112i	$0.0163719\pi$
$158$	2.84967e8	+	1.64526e8i	0.457264	+	0.264001i
$159$		0			0
$160$	−1.78659e8			−0.272612
$161$	−4.33525e6	+	1.07328e7i	−0.00645224	+	0.0159739i
$162$		0			0
$163$	2.17382e8	+	3.76516e8i	0.307944	+	0.533375i	0.977913	−	0.209015i	$-0.0670256\pi$
$163$	2.17382e8	+	3.76516e8i	0.307944	+	0.533375i	−0.669968	+	0.742390i	$0.733692\pi$
$164$	4.46626e8	+	2.57860e8i	0.617403	+	0.356458i
$165$		0			0
$166$	−1.11103e8	−	1.92435e8i	−0.146316	−	0.253427i
$167$		−	1.54057e9i		−	1.98068i	−0.138643	−	0.990342i	$-0.544274\pi$
$167$		−	1.54057e9i		−	1.98068i	0.138643	−	0.990342i	$-0.455726\pi$
$168$		0			0
$169$	1.67623e9			2.05489
$170$	1.12010e9	−	6.46689e8i	1.34110	−	0.774283i
$171$		0			0
$172$	1.49861e7	−	2.59567e7i	0.0171228	−	0.0296576i
$173$	−3.08201e8	+	1.77940e8i	−0.344072	+	0.198650i	−0.662071	−	0.749441i	$-0.730322\pi$
$173$	−3.08201e8	+	1.77940e8i	−0.344072	+	0.198650i	0.317999	+	0.948091i	$0.396989\pi$
$174$		0			0
$175$	1.80001e8	+	1.27996e9i	0.191921	+	1.36472i
$176$		−	2.92559e8i		−	0.304904i
$177$		0			0
$178$	2.90954e8	−	5.03948e8i	0.289831	−	0.502002i
$179$	−7.40642e8	−	4.27610e8i	−0.721433	−	0.416520i	0.0938469	−	0.995587i	$-0.470084\pi$
$179$	−7.40642e8	−	4.27610e8i	−0.721433	−	0.416520i	−0.815280	+	0.579067i	$0.803417\pi$
$180$		0			0
$181$	1.61295e8			0.150282			0.0751409	−	0.997173i	$-0.476059\pi$
$181$	1.61295e8			0.150282			0.0751409	+	0.997173i	$0.476059\pi$
$182$	5.07866e8	−	1.25733e9i	0.462875	−	1.14594i
$183$		0			0
$184$	3.49080e6	+	6.04624e6i	0.00304547	+	0.00527490i
$185$	−2.40486e9	−	1.38845e9i	−2.05307	−	1.18534i
$186$		0			0
$187$	1.05897e9	+	1.83419e9i	0.866000	+	1.49996i
$188$			3.49524e8i			0.279799i
$189$		0			0
$190$	−1.66387e9			−1.27675
$191$	−1.72659e9	+	9.96848e8i	−1.29735	+	0.749023i	−0.979945	−	0.199268i	$-0.936144\pi$
$191$	−1.72659e9	+	9.96848e8i	−1.29735	+	0.749023i	−0.317402	+	0.948291i	$0.602810\pi$
$192$		0			0
$193$	−7.71818e8	+	1.33683e9i	−0.556270	+	0.963488i	0.441534	+	0.897245i	$0.354435\pi$
$193$	−7.71818e8	+	1.33683e9i	−0.556270	+	0.963488i	−0.997804	+	0.0662430i	$0.978899\pi$
$194$	−1.49683e9	+	8.64195e8i	−1.05673	+	0.610105i
$195$		0			0
$196$	−5.30886e8	−	5.12492e8i	−0.359731	−	0.347266i
$197$			4.55264e8i			0.302272i	0.988513	+	0.151136i	$0.0482931\pi$
$197$			4.55264e8i			0.302272i	−0.988513	+	0.151136i	$0.951707\pi$
$198$		0			0
$199$	1.06821e8	−	1.85019e8i	0.0681152	−	0.117979i	−0.829956	−	0.557828i	$-0.811635\pi$
$199$	1.06821e8	−	1.85019e8i	0.0681152	−	0.117979i	0.898072	+	0.439849i	$0.144968\pi$
$200$	6.75153e8	+	3.89800e8i	0.421970	+	0.243625i
$201$		0			0
$202$	8.12097e7			0.0487756
$203$	−7.42327e7	−	9.49964e7i	−0.0437130	−	0.0559401i
$204$		0			0
$205$	−1.94166e9	−	3.36306e9i	−1.09941	−	1.90423i
$206$	−5.51698e8	−	3.18523e8i	−0.306360	−	0.176877i
$207$		0			0
$208$	−4.08941e8	−	7.08307e8i	−0.218478	−	0.378415i
$209$		−	2.72464e9i		−	1.42799i
$210$		0			0
$211$	2.29087e9			1.15577			0.577885	−	0.816118i	$-0.303878\pi$
$211$	2.29087e9			1.15577			0.577885	+	0.816118i	$0.303878\pi$
$212$	1.23983e9	−	7.15815e8i	0.613788	−	0.354371i
$213$		0			0
$214$	7.95183e8	−	1.37730e9i	0.379151	−	0.656709i
$215$	−1.95452e8	+	1.12844e8i	−0.0914715	+	0.0528111i
$216$		0			0
$217$	5.33839e7	+	3.79605e8i	0.0240753	+	0.171196i
$218$			1.36890e9i			0.606104i
$219$		0			0
$220$	−1.10147e9	+	1.90781e9i	−0.470200	+	0.814410i
$221$	5.12770e9	+	2.96048e9i	2.14958	+	1.24106i
$222$		0			0
$223$	−6.42808e8			−0.259933			−0.129967	−	0.991518i	$-0.541487\pi$
$223$	−6.42808e8			−0.259933			−0.129967	+	0.991518i	$0.541487\pi$
$224$	−4.40722e8	+	6.19787e7i	−0.175054	+	0.0246179i
$225$		0			0
$226$	8.41838e8	+	1.45811e9i	0.322697	+	0.558928i
$227$	−6.42102e8	−	3.70718e8i	−0.241825	−	0.139617i	0.374190	−	0.927352i	$-0.377921\pi$
$227$	−6.42102e8	−	3.70718e8i	−0.241825	−	0.139617i	−0.616015	+	0.787734i	$0.711254\pi$
$228$		0			0
$229$	1.63324e9	+	2.82885e9i	0.593893	+	1.02865i	0.993702	+	0.112054i	$0.0357429\pi$
$229$	1.63324e9	+	2.82885e9i	0.593893	+	1.02865i	−0.399809	+	0.916598i	$0.630924\pi$
$230$		−	5.25708e7i		−	0.0187860i
$231$		0			0
$232$	−7.27156e7			−0.0251001
$233$	1.29027e9	−	7.44936e8i	0.437780	−	0.252752i	−0.264876	−	0.964283i	$-0.585331\pi$
$233$	1.29027e9	−	7.44936e8i	0.437780	−	0.252752i	0.702655	+	0.711530i	$0.251998\pi$
$234$		0			0
$235$	1.31594e9	−	2.27928e9i	0.431484	−	0.747353i
$236$	2.07511e9	−	1.19806e9i	0.668949	−	0.386218i
$237$		0			0
$238$	2.53875e9	−	1.98385e9i	0.791248	−	0.618302i
$239$			5.17236e9i			1.58525i	0.609710	+	0.792624i	$0.291286\pi$
$239$			5.17236e9i			1.58525i	−0.609710	+	0.792624i	$0.708714\pi$
$240$		0			0
$241$	−2.03520e9	+	3.52506e9i	−0.603306	+	1.04496i	0.389010	+	0.921233i	$0.372817\pi$
$241$	−2.03520e9	+	3.52506e9i	−0.603306	+	1.04496i	−0.992317	+	0.123724i	$0.960516\pi$
$242$	−1.02381e9	−	5.91096e8i	−0.298509	−	0.172344i
$243$		0			0
$244$	−2.74342e9			−0.773986
$245$	1.53245e9	+	5.34077e9i	0.425326	+	1.48231i
$246$		0			0
$247$	−3.80852e9	−	6.59656e9i	−1.02322	−	1.77227i
$248$	2.00234e8	+	1.15605e8i	0.0529336	+	0.0305612i
$249$		0			0
$250$	−8.05376e8	−	1.39495e9i	−0.206176	−	0.357108i
$251$			3.60204e9i			0.907515i	0.891125	+	0.453757i	$0.149917\pi$
$251$			3.60204e9i			0.907515i	−0.891125	+	0.453757i	$0.850083\pi$
$252$		0			0
$253$	8.60863e7			0.0210112
$254$	4.34498e9	−	2.50858e9i	1.04389	−	0.602688i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−2.26915e9	+	1.31009e9i	−0.520152	+	0.300310i	−0.736997	−	0.675896i	$-0.763757\pi$
$257$	−2.26915e9	+	1.31009e9i	−0.520152	+	0.300310i	0.216845	+	0.976206i	$0.430423\pi$
$258$		0			0
$259$	−6.41406e9	−	2.59080e9i	−1.42539	−	0.575751i
$260$			6.15858e9i			1.34768i
$261$		0			0
$262$	1.61936e8	−	2.80482e8i	0.0343668	−	0.0595250i
$263$	−3.41077e9	−	1.96921e9i	−0.712902	−	0.411594i	0.0992325	−	0.995064i	$-0.468361\pi$
$263$	−3.41077e9	−	1.96921e9i	−0.712902	−	0.411594i	−0.812135	+	0.583470i	$0.801695\pi$
$264$		0			0
$265$	−1.07800e10			−2.18594
$266$	−4.10450e9	+	5.77216e8i	−0.819849	+	0.115295i
$267$		0			0
$268$	1.80410e9	+	3.12480e9i	0.349721	+	0.605735i
$269$	−3.26482e9	−	1.88495e9i	−0.623520	−	0.359989i	0.154718	−	0.987959i	$-0.450553\pi$
$269$	−3.26482e9	−	1.88495e9i	−0.623520	−	0.359989i	−0.778238	+	0.627969i	$0.783886\pi$
$270$		0			0
$271$	1.06929e9	+	1.85206e9i	0.198252	+	0.343382i	0.947962	−	0.318385i	$-0.103140\pi$
$271$	1.06929e9	+	1.85206e9i	0.198252	+	0.343382i	−0.749710	+	0.661766i	$0.769807\pi$
$272$		−	1.94330e9i		−	0.355030i
$273$		0			0
$274$	3.22597e9			0.572345
$275$	8.32494e9	−	4.80640e9i	1.45563	−	0.840407i
$276$		0			0
$277$	−1.25751e9	+	2.17807e9i	−0.213595	+	0.369958i	−0.952837	−	0.303482i	$-0.901851\pi$
$277$	−1.25751e9	+	2.17807e9i	−0.213595	+	0.369958i	0.739242	+	0.673440i	$0.235184\pi$
$278$	−4.86591e9	+	2.80933e9i	−0.814676	+	0.470353i
$279$		0			0
$280$	3.10733e9	+	1.25513e9i	0.505540	+	0.204200i
$281$			1.00710e10i			1.61528i	0.589678	+	0.807638i	$0.299255\pi$
$281$			1.00710e10i			1.61528i	−0.589678	+	0.807638i	$0.700745\pi$
$282$		0			0
$283$	3.84978e9	−	6.66801e9i	0.600191	−	1.03956i	−0.392600	−	0.919709i	$-0.628424\pi$
$283$	3.84978e9	−	6.66801e9i	0.600191	−	1.03956i	0.992792	−	0.119853i	$-0.0382423\pi$
$284$	−1.62457e9	−	9.37946e8i	−0.249727	−	0.144180i
$285$		0			0
$286$	−1.00849e10			−1.50732
$287$	−5.95644e9	−	7.62252e9i	−0.877928	−	1.12349i
$288$		0			0
$289$	3.54627e9	+	6.14231e9i	0.508370	+	0.880523i
$290$	4.74185e8	+	2.73771e8i	0.0670434	+	0.0387075i
$291$		0			0
$292$	1.60128e9	+	2.77350e9i	0.220260	+	0.381501i
$293$		−	6.33431e9i		−	0.859466i	−0.902956	−	0.429733i	$-0.858608\pi$
$293$		−	6.33431e9i		−	0.859466i	0.902956	−	0.429733i	$-0.141392\pi$
$294$		0			0
$295$	−1.80426e10			−2.38238
$296$	−3.61331e9	+	2.08615e9i	−0.470694	+	0.271755i
$297$		0			0
$298$	1.97977e9	−	3.42907e9i	0.251044	−	0.434821i
$299$	2.08421e8	−	1.20332e8i	0.0260770	−	0.0150555i
$300$		0			0
$301$	−4.43000e8	+	3.46172e8i	−0.0539682	+	0.0421722i
$302$		−	2.75981e9i		−	0.331781i
$303$		0			0
$304$	−1.24999e9	+	2.16504e9i	−0.146356	+	0.253497i
$305$	1.78901e10	+	1.03288e10i	2.06735	+	1.19358i
$306$		0			0
$307$	1.30278e10			1.46662			0.733312	−	0.679892i	$-0.237974\pi$
$307$	1.30278e10			1.46662			0.733312	+	0.679892i	$0.237974\pi$
$308$	−2.05531e9	+	5.08835e9i	−0.228389	+	0.565424i
$309$		0			0
$310$	−8.70497e8	−	1.50775e9i	−0.0942585	−	0.163261i
$311$	4.30918e9	+	2.48791e9i	0.460631	+	0.265945i	0.712310	−	0.701865i	$-0.247649\pi$
$311$	4.30918e9	+	2.48791e9i	0.460631	+	0.265945i	−0.251679	+	0.967811i	$0.580983\pi$
$312$		0			0
$313$	2.33214e9	+	4.03939e9i	0.242984	+	0.420861i	0.961563	−	0.274585i	$-0.0885403\pi$
$313$	2.33214e9	+	4.03939e9i	0.242984	+	0.420861i	−0.718579	+	0.695446i	$0.755207\pi$
$314$			6.25272e9i			0.643206i
$315$		0			0
$316$	−3.72280e9			−0.373354
$317$	−1.21222e10	+	6.99877e9i	−1.20045	+	0.693082i	−0.960656	−	0.277741i	$-0.910414\pi$
$317$	−1.21222e10	+	6.99877e9i	−1.20045	+	0.693082i	−0.239797	+	0.970823i	$0.577081\pi$
$318$		0			0
$319$	−4.48308e8	+	7.76492e8i	−0.0432926	+	0.0749850i
$320$	1.75049e9	−	1.01065e9i	0.166940	−	0.0963828i
$321$		0			0
$322$	−1.82374e7	−	1.29683e8i	−0.00169644	−	0.0120632i
$323$		−	1.80982e10i		−	1.66275i
$324$		0			0
$325$	1.34368e10	−	2.32733e10i	1.20438	−	2.08605i
$326$	−4.25979e9	−	2.45939e9i	−0.377153	−	0.217750i
$327$		0			0
$328$	−5.83470e9			−0.504108
$329$	2.45550e9	−	6.07911e9i	0.209583	−	0.518868i
$330$		0			0
$331$	−6.95467e9	−	1.20458e10i	−0.579382	−	1.00352i	−0.995550	−	0.0942310i	$-0.969961\pi$
$331$	−6.95467e9	−	1.20458e10i	−0.579382	−	1.00352i	0.416169	−	0.909287i	$-0.363373\pi$
$332$	2.17716e9	+	1.25698e9i	0.179200	+	0.103461i
$333$		0			0
$334$	8.71478e9	+	1.50944e10i	0.700278	+	1.21292i
$335$		−	2.71695e10i		−	2.15726i
$336$		0			0
$337$	1.47127e10			1.14071			0.570353	−	0.821400i	$-0.306806\pi$
$337$	1.47127e10			1.14071			0.570353	+	0.821400i	$0.306806\pi$
$338$	−1.64237e10	+	9.48221e9i	−1.25836	+	0.726512i
$339$		0			0
$340$	−7.31645e9	+	1.26725e10i	−0.547501	+	0.948299i
$341$	2.46898e9	−	1.42546e9i	0.182600	−	0.105424i
$342$		0			0
$343$	5.63307e9	+	1.26432e10i	0.406976	+	0.913439i
$344$			3.39097e8i			0.0242153i
$345$		0			0
$346$	2.01316e9	−	3.48689e9i	0.140467	−	0.243295i
$347$	1.61664e10	+	9.33367e9i	1.11505	+	0.643776i	0.940133	−	0.340807i	$-0.110700\pi$
$347$	1.61664e10	+	9.33367e9i	1.11505	+	0.643776i	0.174919	+	0.984583i	$0.444034\pi$
$348$		0			0
$349$	−1.52813e10			−1.03005			−0.515026	−	0.857175i	$-0.672218\pi$
$349$	−1.52813e10			−1.03005			−0.515026	+	0.857175i	$0.672218\pi$
$350$	−9.00418e9	−	1.15227e10i	−0.600029	−	0.767863i
$351$		0			0
$352$	1.65496e9	+	2.86648e9i	0.107800	+	0.186715i
$353$	2.48283e8	+	1.43346e8i	0.0159900	+	0.00923184i	0.507974	−	0.861373i	$-0.330395\pi$
$353$	2.48283e8	+	1.43346e8i	0.0159900	+	0.00923184i	−0.491984	+	0.870604i	$0.663728\pi$
$354$		0			0
$355$	7.06265e9	+	1.22329e10i	0.444687	+	0.770220i
$356$			6.58355e9i			0.409883i
$357$		0			0
$358$	9.67570e9			0.589048
$359$	6.38395e9	−	3.68577e9i	0.384336	−	0.221897i	−0.295367	−	0.955384i	$-0.595442\pi$
$359$	6.38395e9	−	3.68577e9i	0.384336	−	0.221897i	0.679703	+	0.733487i	$0.262109\pi$
$360$		0			0
$361$	−3.14952e9	+	5.45513e9i	−0.185445	+	0.321200i
$362$	−1.58036e9	+	9.12421e8i	−0.0920284	+	0.0531326i
$363$		0			0
$364$	2.13648e9	+	1.51922e10i	0.121701	+	0.865396i
$365$		−	2.41150e10i		−	1.35867i
$366$		0			0
$367$	2.09895e9	−	3.63548e9i	0.115701	−	0.200400i	−0.802359	−	0.596842i	$-0.796422\pi$
$367$	2.09895e9	−	3.63548e9i	0.115701	−	0.200400i	0.918060	+	0.396442i	$0.129755\pi$
$368$	−6.84054e7	−	3.94939e7i	−0.00372992	−	0.00215347i
$369$		0			0
$370$	3.14170e10			1.67632
$371$	−2.65926e10	+	3.73972e9i	−1.40367	+	0.197398i
$372$		0			0
$373$	8.31690e9	+	1.44053e10i	0.429661	+	0.744195i	0.996843	−	0.0793974i	$-0.0252996\pi$
$373$	8.31690e9	+	1.44053e10i	0.429661	+	0.744195i	−0.567182	+	0.823593i	$0.691966\pi$
$374$	−2.07515e10	−	1.19809e10i	−1.06063	−	0.612355i
$375$		0			0
$376$	−1.97721e9	−	3.42462e9i	−0.0989237	−	0.171341i
$377$			2.50659e9i			0.124085i
$378$		0			0
$379$	−1.53020e10			−0.741638			−0.370819	−	0.928705i	$-0.620923\pi$
$379$	−1.53020e10			−0.741638			−0.370819	+	0.928705i	$0.620923\pi$
$380$	1.63026e10	−	9.41229e9i	0.781847	−	0.451399i
$381$		0			0
$382$	1.12780e10	−	1.95341e10i	0.529640	−	0.917363i
$383$	3.22985e10	−	1.86475e10i	1.50102	−	0.866616i	0.501023	−	0.865434i	$-0.332957\pi$
$383$	3.22985e10	−	1.86475e10i	1.50102	−	0.866616i	0.999999	−	0.00118182i	$-0.000376185\pi$
$384$		0			0
$385$	3.25603e10	−	2.54435e10i	1.48199	−	1.15807i
$386$		−	1.74642e10i		−	0.786684i
$387$		0			0
$388$	9.77725e9	−	1.69347e10i	0.431410	−	0.747223i
$389$	−2.32607e9	−	1.34296e9i	−0.101584	−	0.0586493i	0.448348	−	0.893859i	$-0.352013\pi$
$389$	−2.32607e9	−	1.34296e9i	−0.101584	−	0.0586493i	−0.549931	+	0.835210i	$0.685346\pi$
$390$		0			0
$391$	5.71822e8			0.0244655
$392$	8.10070e9	+	2.01823e9i	0.343066	+	0.0854724i
$393$		0			0
$394$	−2.57536e9	−	4.46065e9i	−0.106869	−	0.185103i
$395$	2.42767e10	+	1.40162e10i	0.997244	+	0.575759i
$396$		0			0
$397$	−5.84760e9	−	1.01283e10i	−0.235405	−	0.407733i	0.723985	−	0.689815i	$-0.242308\pi$
$397$	−5.84760e9	−	1.01283e10i	−0.235405	−	0.407733i	−0.959390	+	0.282082i	$0.908975\pi$
$398$			2.41708e9i			0.0963294i
$399$		0			0
$400$	−8.82016e9			−0.344537
$401$	6.27577e9	−	3.62332e9i	0.242711	−	0.140129i	−0.373711	−	0.927545i	$-0.621915\pi$
$401$	6.27577e9	−	3.62332e9i	0.242711	−	0.140129i	0.616422	+	0.787416i	$0.288582\pi$
$402$		0			0
$403$	3.98505e9	−	6.90231e9i	0.151082	−	0.261682i
$404$	−7.95689e8	+	4.59391e8i	−0.0298688	+	0.0172448i
$405$		0			0
$406$	1.26471e9	+	5.10847e8i	0.0465465	+	0.0188013i
$407$			5.14463e10i			1.87489i
$408$		0			0
$409$	1.64602e10	−	2.85098e10i	0.588222	−	1.01883i	−0.406244	−	0.913765i	$-0.633162\pi$
$409$	1.64602e10	−	2.85098e10i	0.588222	−	1.01883i	0.994465	−	0.105065i	$-0.0335051\pi$
$410$	3.80486e10	+	2.19674e10i	1.34649	+	0.777397i
$411$		0			0
$412$	7.20735e9			0.250142
$413$	−4.45082e10	+	6.25918e9i	−1.52982	+	0.215138i
$414$		0			0
$415$	−9.46496e9	−	1.63938e10i	−0.319100	−	0.552697i
$416$	8.01358e9	+	4.62664e9i	0.267580	+	0.154487i
$417$		0			0
$418$	1.54129e10	+	2.66959e10i	0.504870	+	0.874460i
$419$			3.09437e10i			1.00396i	0.864879	+	0.501980i	$0.167395\pi$
$419$			3.09437e10i			1.00396i	−0.864879	+	0.501980i	$0.832605\pi$
$420$		0			0
$421$	−2.95841e10			−0.941737			−0.470868	−	0.882203i	$-0.656059\pi$
$421$	−2.95841e10			−0.941737			−0.470868	+	0.882203i	$0.656059\pi$
$422$	−2.24459e10	+	1.29591e10i	−0.707762	+	0.408626i
$423$		0			0
$424$	−8.09853e9	+	1.40271e10i	−0.250578	+	0.434014i
$425$	5.52978e10	−	3.19262e10i	1.69493	−	0.978569i
$426$		0			0
$427$	4.77151e10	+	1.92733e10i	1.43530	+	0.579755i
$428$			1.79929e10i			0.536200i
$429$		0			0
$430$	1.27669e9	−	2.21129e9i	0.0373431	−	0.0646801i
$431$	−4.29263e10	−	2.47835e10i	−1.24398	−	0.718214i	−0.274080	−	0.961707i	$-0.588373\pi$
$431$	−4.29263e10	−	2.47835e10i	−1.24398	−	0.718214i	−0.969903	+	0.243493i	$0.921707\pi$
$432$		0			0
$433$	1.00408e9			0.0285638			0.0142819	−	0.999898i	$-0.495454\pi$
$433$	1.00408e9			0.0285638			0.0142819	+	0.999898i	$0.495454\pi$
$434$	−2.67043e9	−	3.41737e9i	−0.0752699	−	0.0963238i
$435$		0			0
$436$	−7.74369e9	−	1.34125e10i	−0.214290	−	0.371161i
$437$	−6.37069e8	−	3.67812e8i	−0.0174687	−	0.0100856i
$438$		0			0
$439$	1.08479e10	+	1.87892e10i	0.292071	+	0.505883i	0.974299	−	0.225257i	$-0.0723222\pi$
$439$	1.08479e10	+	1.87892e10i	0.292071	+	0.505883i	−0.682228	+	0.731140i	$0.738989\pi$
$440$		−	2.49235e10i		−	0.664963i
$441$		0			0
$442$	−6.69879e10			−1.75512
$443$	2.49251e10	−	1.43905e10i	0.647174	−	0.373646i	−0.140198	−	0.990123i	$-0.544774\pi$
$443$	2.49251e10	−	1.43905e10i	0.647174	−	0.373646i	0.787373	+	0.616477i	$0.211441\pi$
$444$		0			0
$445$	2.47868e10	−	4.29319e10i	0.632091	−	1.09481i
$446$	6.29820e9	−	3.63627e9i	0.159176	−	0.0919002i
$447$		0			0
$448$	3.96757e9	−	3.10036e9i	0.0984946	−	0.0769663i
$449$			2.46180e10i			0.605713i	0.953036	+	0.302856i	$0.0979403\pi$
$449$			2.46180e10i			0.605713i	−0.953036	+	0.302856i	$0.902060\pi$
$450$		0			0
$451$	−3.59722e10	+	6.23058e10i	−0.869484	+	1.50599i
$452$	−1.64966e10	−	9.52431e9i	−0.395221	−	0.228181i
$453$		0			0
$454$	8.38838e9			0.197449
$455$	4.32657e10	−	1.07113e11i	1.00948	−	2.49918i
$456$		0			0
$457$	2.71669e10	+	4.70544e10i	0.622838	+	1.07879i	0.988955	+	0.148218i	$0.0473538\pi$
$457$	2.71669e10	+	4.70544e10i	0.622838	+	1.07879i	−0.366117	+	0.930569i	$0.619313\pi$
$458$	−3.20048e10	−	1.84780e10i	−0.727367	−	0.419946i
$459$		0			0
$460$	2.97385e8	+	5.15087e8i	0.00664184	+	0.0115040i
$461$			4.39361e10i			0.972787i	0.873740	+	0.486393i	$0.161688\pi$
$461$			4.39361e10i			0.972787i	−0.873740	+	0.486393i	$0.838312\pi$
$462$		0			0
$463$	−6.47397e10			−1.40879			−0.704396	−	0.709808i	$-0.748782\pi$
$463$	−6.47397e10			−1.40879			−0.704396	+	0.709808i	$0.748782\pi$
$464$	7.12464e8	−	4.11341e8i	0.0153706	−	0.00887423i
$465$		0			0
$466$	−8.42799e9	+	1.45977e10i	−0.178723	+	0.309557i
$467$	−4.61022e10	+	2.66171e10i	−0.969290	+	0.559620i	−0.899020	−	0.437908i	$-0.855720\pi$
$467$	−4.61022e10	+	2.66171e10i	−0.969290	+	0.559620i	−0.0702705	+	0.997528i	$0.522386\pi$
$468$		0			0
$469$	−9.42538e9	−	6.70225e10i	−0.194808	−	1.38525i
$470$			2.97764e10i			0.610211i
$471$		0			0
$472$	−1.35545e10	+	2.34772e10i	−0.273097	+	0.473018i
$473$	3.62105e9	+	2.09061e9i	0.0723418	+	0.0417666i
$474$		0			0
$475$	−8.21433e10			−1.61361
$476$	−1.36523e10	+	3.37990e10i	−0.265936	+	0.658379i
$477$		0			0
$478$	−2.92593e10	−	5.06786e10i	−0.560470	−	0.970763i
$479$	−7.64834e10	−	4.41577e10i	−1.45286	−	0.838812i	−0.454221	−	0.890889i	$-0.650082\pi$
$479$	−7.64834e10	−	4.41577e10i	−1.45286	−	0.838812i	−0.998643	+	0.0520774i	$0.983416\pi$
$480$		0			0
$481$	7.19119e10	+	1.24555e11i	1.34345	+	2.32692i
$482$		−	4.60512e10i		−	0.853204i
$483$		0			0
$484$	1.33750e10			0.243731
$485$	−1.27517e11	+	7.36218e10i	−2.30462	+	1.33058i
$486$		0			0
$487$	−4.82749e10	+	8.36146e10i	−0.858233	+	1.48650i	0.0153791	+	0.999882i	$0.495104\pi$
$487$	−4.82749e10	+	8.36146e10i	−0.858233	+	1.48650i	−0.873613	+	0.486622i	$0.838229\pi$
$488$	2.68799e10	−	1.55191e10i	0.473967	−	0.273645i
$489$		0			0
$490$	−4.52268e10	−	4.36598e10i	−0.784534	−	0.757351i
$491$			6.98650e10i			1.20208i	0.799219	+	0.601040i	$0.205247\pi$
$491$			6.98650e10i			1.20208i	−0.799219	+	0.601040i	$0.794753\pi$
$492$		0			0
$493$	−2.97785e9	+	5.15779e9i	−0.0504099	+	0.0873124i
$494$	7.46315e10	+	4.30885e10i	1.25318	+	0.723526i
$495$		0			0
$496$	−2.61585e9			−0.0432201
$497$	2.16661e10	+	2.77263e10i	0.355104	+	0.454430i
$498$		0			0
$499$	−4.01148e10	−	6.94809e10i	−0.646997	−	1.12063i	−0.983836	−	0.179070i	$-0.942691\pi$
$499$	−4.01148e10	−	6.94809e10i	−0.646997	−	1.12063i	0.336839	−	0.941562i	$-0.390642\pi$
$500$	1.57821e10	+	9.11179e9i	0.252513	+	0.145789i
$501$		0			0
$502$	−2.03762e10	−	3.52927e10i	−0.320855	−	0.555737i
$503$			7.31387e9i			0.114255i	0.998367	+	0.0571275i	$0.0181942\pi$
$503$			7.31387e9i			0.114255i	−0.998367	+	0.0571275i	$0.981806\pi$
$504$		0			0
$505$	6.91835e9			0.106374
$506$	−8.43470e8	+	4.86977e8i	−0.0128667	+	0.00742860i
$507$		0			0
$508$	−2.83813e10	+	4.91579e10i	−0.426165	+	0.738139i
$509$	−3.64500e10	+	2.10444e10i	−0.543034	+	0.313521i	−0.746308	−	0.665601i	$-0.768175\pi$
$509$	−3.64500e10	+	2.10444e10i	−0.543034	+	0.313521i	0.203274	+	0.979122i	$0.434842\pi$
$510$		0			0
$511$	−8.36574e9	−	5.94876e10i	−0.122693	−	0.872455i
$512$		−	3.03700e9i		−	0.0441942i
$513$		0			0
$514$	1.48220e10	−	2.56725e10i	0.212351	−	0.367803i
$515$	−4.69998e10	−	2.71353e10i	−0.668139	−	0.385750i
$516$		0			0
$517$	−4.87597e10			−0.682493
$518$	7.75005e10	−	1.08989e10i	1.07643	−	0.151378i
$519$		0			0
$520$	−3.48382e10	−	6.03415e10i	−0.476477	−	0.825283i
$521$	−1.55559e9	−	8.98120e8i	−0.0211127	−	0.0121894i	0.489406	−	0.872056i	$-0.337213\pi$
$521$	−1.55559e9	−	8.98120e8i	−0.0211127	−	0.0121894i	−0.510519	+	0.859866i	$0.670547\pi$
$522$		0			0
$523$	−1.20271e9	−	2.08315e9i	−0.0160751	−	0.0278429i	0.857876	−	0.513857i	$-0.171784\pi$
$523$	−1.20271e9	−	2.08315e9i	−0.0160751	−	0.0278429i	−0.873951	+	0.486014i	$0.838450\pi$
$524$			3.66420e9i			0.0486020i
$525$		0			0
$526$	4.45582e10			0.582082
$527$	1.64000e10	−	9.46855e9i	0.212619	−	0.122755i
$528$		0			0
$529$	−3.91439e10	+	6.77992e10i	−0.499852	+	0.865768i
$530$	1.05622e11	−	6.09812e10i	1.33861	−	0.772845i
$531$		0			0
$532$	3.69505e10	−	2.88741e10i	0.461290	−	0.360464i
$533$			2.01129e11i			2.49210i
$534$		0			0
$535$	6.77426e10	−	1.17334e11i	0.826888	−	1.43221i
$536$	−3.53531e10	−	2.04111e10i	−0.428319	−	0.247290i
$537$		0			0
$538$	4.26514e10			0.509102
$539$	7.14942e10	−	7.40603e10i	0.847063	−	0.877466i
$540$		0			0
$541$	−3.67093e10	−	6.35824e10i	−0.428536	−	0.742246i	0.568208	−	0.822885i	$-0.307637\pi$
$541$	−3.67093e10	−	6.35824e10i	−0.428536	−	0.742246i	−0.996743	+	0.0806397i	$0.974304\pi$
$542$	−2.09536e10	−	1.20976e10i	−0.242808	−	0.140185i
$543$		0			0
$544$	1.09930e10	+	1.90404e10i	0.125522	+	0.217411i
$545$			1.16619e11i			1.32185i
$546$		0			0
$547$	−1.41950e11			−1.58558			−0.792788	−	0.609498i	$-0.791371\pi$
$547$	−1.41950e11			−1.58558			−0.792788	+	0.609498i	$0.791371\pi$
$548$	−3.16079e10	+	1.82488e10i	−0.350488	+	0.202354i
$549$		0			0
$550$	−5.43783e10	+	9.41859e10i	−0.594257	+	1.02928i
$551$	6.63527e9	−	3.83088e9i	0.0719867	−	0.0415616i
$552$		0			0
$553$	6.47490e10	+	2.61537e10i	0.692361	+	0.279662i
$554$		−	2.84542e10i		−	0.302070i
$555$		0			0
$556$	3.17840e10	−	5.50515e10i	0.332590	−	0.576063i
$557$	4.91149e10	+	2.83565e10i	0.510261	+	0.294600i	0.732941	−	0.680292i	$-0.238147\pi$
$557$	4.91149e10	+	2.83565e10i	0.510261	+	0.294600i	−0.222680	+	0.974892i	$0.571480\pi$
$558$		0			0
$559$	1.16891e10			0.119711
$560$	−3.75456e10	+	5.28004e9i	−0.381775	+	0.0536889i
$561$		0			0
$562$	−5.69701e10	−	9.86752e10i	−0.571087	−	0.989151i
$563$	−8.72568e10	−	5.03777e10i	−0.868492	−	0.501424i	−0.00164490	−	0.999999i	$-0.500524\pi$
$563$	−8.72568e10	−	5.03777e10i	−0.868492	−	0.501424i	−0.866847	+	0.498575i	$0.833857\pi$
$564$		0			0
$565$	7.17172e10	+	1.24218e11i	0.703768	+	1.21896i
$566$			8.71105e10i			0.848799i
$567$		0			0
$568$	2.12233e10			0.203901
$569$	−8.92860e8	+	5.15493e8i	−0.00851794	+	0.00491783i	−0.504253	−	0.863556i	$-0.668232\pi$
$569$	−8.92860e8	+	5.15493e8i	−0.00851794	+	0.00491783i	0.495735	+	0.868474i	$0.334899\pi$
$570$		0			0
$571$	−4.97756e10	+	8.62139e10i	−0.468244	+	0.811022i	−0.999341	−	0.0362886i	$-0.988446\pi$
$571$	−4.97756e10	+	8.62139e10i	−0.468244	+	0.811022i	0.531098	+	0.847311i	$0.321780\pi$
$572$	9.88110e10	−	5.70486e10i	0.923041	−	0.532918i
$573$		0			0
$574$	1.01480e11	+	4.09904e10i	0.934834	+	0.377602i
$575$		−	2.59535e9i		−	0.0237424i
$576$		0			0
$577$	−9.37422e9	+	1.62366e10i	−0.0845730	+	0.146485i	−0.905209	−	0.424966i	$-0.860286\pi$
$577$	−9.37422e9	+	1.62366e10i	−0.0845730	+	0.146485i	0.820636	+	0.571451i	$0.193619\pi$
$578$	−6.94923e10	−	4.01214e10i	−0.622624	−	0.359472i
$579$		0			0
$580$	−6.19473e9			−0.0547407
$581$	−2.90357e10	−	3.71573e10i	−0.254816	−	0.326091i
$582$		0			0
$583$	9.98585e10	+	1.72960e11i	0.864392	+	1.49717i
$584$	−3.13785e10	−	1.81164e10i	−0.269762	−	0.155747i
$585$		0			0
$586$	3.58323e10	+	6.20633e10i	0.303867	+	0.526313i
$587$		−	1.17838e11i		−	0.992506i	−0.868178	−	0.496253i	$-0.834709\pi$
$587$		−	1.17838e11i		−	0.992506i	0.868178	−	0.496253i	$-0.165291\pi$
$588$		0			0
$589$	−2.43617e10			−0.202417
$590$	1.76781e11	−	1.02065e11i	1.45891	−	0.842300i
$591$		0			0
$592$	2.36021e10	−	4.08800e10i	0.192160	−	0.332831i
$593$	8.20341e10	−	4.73624e10i	0.663400	−	0.383014i	−0.130171	−	0.991492i	$-0.541553\pi$
$593$	8.20341e10	−	4.73624e10i	0.663400	−	0.383014i	0.793571	+	0.608477i	$0.208219\pi$
$594$		0			0
$595$	2.16279e11	−	1.69006e11i	1.72563	−	1.34845i
$596$			4.47971e10i			0.355030i
$597$		0			0
$598$	−1.36140e9	+	2.35802e9i	−0.0106459	+	0.0184392i
$599$	4.97673e10	+	2.87331e10i	0.386577	+	0.223191i	0.680676	−	0.732584i	$-0.261686\pi$
$599$	4.97673e10	+	2.87331e10i	0.386577	+	0.223191i	−0.294099	+	0.955775i	$0.595019\pi$
$600$		0			0
$601$	1.31488e11			1.00783			0.503917	−	0.863752i	$-0.331892\pi$
$601$	1.31488e11			1.00783			0.503917	+	0.863752i	$0.331892\pi$
$602$	2.38225e9	−	5.89777e9i	0.0181385	−	0.0449057i
$603$		0			0
$604$	1.56118e10	+	2.70405e10i	0.117302	+	0.203173i
$605$	−8.72194e10	−	5.03562e10i	−0.651016	−	0.375864i
$606$		0			0
$607$	−2.65304e10	−	4.59521e10i	−0.195429	−	0.338494i	0.751612	−	0.659606i	$-0.229277\pi$
$607$	−2.65304e10	−	4.59521e10i	−0.195429	−	0.338494i	−0.947041	+	0.321112i	$0.895943\pi$
$608$		−	2.82840e10i		−	0.206979i
$609$		0			0
$610$	−2.33715e11			−1.68798
$611$	−1.18051e11	+	6.81566e10i	−0.847039	+	0.489038i
$612$		0			0
$613$	−1.47414e10	+	2.55329e10i	−0.104399	+	0.180825i	−0.913493	−	0.406855i	$-0.866625\pi$
$613$	−1.47414e10	+	2.55329e10i	−0.104399	+	0.180825i	0.809093	+	0.587680i	$0.199959\pi$
$614$	−1.27646e11	+	7.36966e10i	−0.898120	+	0.518530i
$615$		0			0
$616$	−8.64622e9	−	6.14821e10i	−0.0600487	−	0.426998i
$617$		−	6.49437e10i		−	0.448122i	−0.974575	−	0.224061i	$-0.928069\pi$
$617$		−	6.49437e10i		−	0.448122i	0.974575	−	0.224061i	$-0.0719315\pi$
$618$		0			0
$619$	7.53440e10	−	1.30500e11i	0.513199	−	0.888887i	−0.486684	−	0.873578i	$-0.661794\pi$
$619$	7.53440e10	−	1.30500e11i	0.513199	−	0.888887i	0.999883	−	0.0153085i	$-0.00487305\pi$
$620$	1.70582e10	+	9.84855e9i	0.115443	+	0.0666508i
$621$		0			0
$622$	−5.62949e10			−0.376104
$623$	4.62513e10	−	1.14505e11i	0.307023	−	0.760101i
$624$		0			0
$625$	3.65336e10	+	6.32780e10i	0.239426	+	0.414699i
$626$	−4.57005e10	−	2.63852e10i	−0.297594	−	0.171816i
$627$		0			0
$628$	−3.53707e10	−	6.12639e10i	−0.227408	−	0.393882i
$629$			3.41728e11i			2.18312i
$630$		0			0
$631$	6.89131e9			0.0434695			0.0217347	−	0.999764i	$-0.493081\pi$
$631$	6.89131e9			0.0434695			0.0217347	+	0.999764i	$0.493081\pi$
$632$	3.64758e10	−	2.10593e10i	0.228632	−	0.132001i
$633$		0			0
$634$	7.91820e10	−	1.37147e11i	0.490083	−	0.848849i
$635$	3.70154e11	−	2.13709e11i	2.27661	−	1.31440i
$636$		0			0
$637$	6.95706e10	−	2.79240e11i	0.422540	−	1.69598i
$638$		−	1.01440e10i		−	0.0612250i
$639$		0			0
$640$	−1.14342e10	+	1.98046e10i	−0.0681529	+	0.118044i
$641$	−2.47574e10	−	1.42937e10i	−0.146647	−	0.0846665i	0.424881	−	0.905249i	$-0.360316\pi$
$641$	−2.47574e10	−	1.42937e10i	−0.146647	−	0.0846665i	−0.571528	+	0.820583i	$0.693649\pi$
$642$		0			0
$643$	5.76586e10			0.337303			0.168652	−	0.985676i	$-0.446059\pi$
$643$	5.76586e10			0.337303			0.168652	+	0.985676i	$0.446059\pi$
$644$	9.12290e8	+	1.16747e9i	0.00530383	+	0.00678736i
$645$		0			0
$646$	1.02379e11	+	1.77326e11i	0.587870	+	1.01822i
$647$	−1.51652e11	−	8.75564e10i	−0.865429	−	0.499656i	0.000397304	−	1.00000i	$-0.499874\pi$
$647$	−1.51652e11	−	8.75564e10i	−0.865429	−	0.499656i	−0.865827	+	0.500344i	$0.833207\pi$
$648$		0			0
$649$	1.67134e11	+	2.89484e11i	0.942074	+	1.63172i
$650$			3.04041e11i			1.70325i
$651$		0			0
$652$	5.56497e10			0.307944
$653$	1.26526e11	−	7.30496e10i	0.695866	−	0.401759i	−0.109940	−	0.993938i	$-0.535066\pi$
$653$	1.26526e11	−	7.30496e10i	0.695866	−	0.401759i	0.805806	+	0.592180i	$0.201732\pi$
$654$		0			0
$655$	1.37955e10	−	2.38946e10i	0.0749503	−	0.129818i
$656$	5.71682e10	−	3.30061e10i	0.308702	−	0.178229i
$657$		0			0
$658$	1.03297e10	+	7.34533e10i	0.0551043	+	0.391839i
$659$		−	3.10474e11i		−	1.64621i	−0.567892	−	0.823103i	$-0.692241\pi$
$659$		−	3.10474e11i		−	1.64621i	0.567892	−	0.823103i	$-0.307759\pi$
$660$		0			0
$661$	9.24973e10	−	1.60210e11i	0.484533	−	0.839235i	−0.515310	−	0.857004i	$-0.672323\pi$
$661$	9.24973e10	−	1.60210e11i	0.484533	−	0.839235i	0.999842	+	0.0177691i	$0.00565637\pi$
$662$	1.36283e11	+	7.86831e10i	0.709595	+	0.409685i
$663$		0			0
$664$	−2.84423e10			−0.146316
$665$	−3.49667e11	+	4.91737e10i	−1.78800	+	0.251447i
$666$		0			0
$667$	1.21038e8	+	2.09644e8i	0.000611532	+	0.00105920i
$668$	−1.70774e11	−	9.85964e10i	−0.857662	−	0.495171i
$669$		0			0
$670$	1.53694e11	+	2.66205e11i	0.762705	+	1.32104i
$671$		−	3.82715e11i		−	1.88793i
$672$		0			0
$673$	1.07677e11			0.524885			0.262443	−	0.964948i	$-0.415472\pi$
$673$	1.07677e11			0.524885			0.262443	+	0.964948i	$0.415472\pi$
$674$	−1.44155e11	+	8.32278e10i	−0.698537	+	0.403301i
$675$		0			0
$676$	1.07279e11	−	1.85813e11i	0.513722	−	0.889792i
$677$	1.53131e11	−	8.84104e10i	0.728969	−	0.420871i	−0.0890757	−	0.996025i	$-0.528391\pi$
$677$	1.53131e11	−	8.84104e10i	0.728969	−	0.420871i	0.818045	+	0.575154i	$0.195058\pi$
$678$		0			0
$679$	−2.89022e11	+	2.25850e11i	−1.35973	+	1.06253i
$680$		−	1.65552e11i		−	0.774283i
$681$		0			0
$682$	−1.61273e10	+	2.79333e10i	−0.0745459	+	0.129117i
$683$	−2.25504e11	−	1.30195e11i	−1.03627	−	0.598288i	−0.117492	−	0.993074i	$-0.537486\pi$
$683$	−2.25504e11	−	1.30195e11i	−1.03627	−	0.598288i	−0.918773	+	0.394785i	$0.870819\pi$
$684$		0			0
$685$	2.74824e11			1.24822
$686$	−1.26713e11	−	9.20118e10i	−0.572170	−	0.415477i
$687$		0			0
$688$	−1.91822e9	−	3.32246e9i	−0.00856142	−	0.0148288i
$689$	4.83529e11	+	2.79166e11i	2.14559	+	1.23875i
$690$		0			0
$691$	4.74443e10	+	8.21759e10i	0.208100	+	0.360439i	0.951116	−	0.308834i	$-0.0999388\pi$
$691$	4.74443e10	+	8.21759e10i	0.208100	+	0.360439i	−0.743016	+	0.669273i	$0.766605\pi$
$692$			4.55525e10i			0.198650i
$693$		0			0
$694$	−2.11197e11			−0.910436
$695$	−4.14533e11	+	2.39331e11i	−1.77672	+	1.02579i
$696$		0			0
$697$	−2.38943e11	+	4.13862e11i	−1.01243	+	1.75357i
$698$	1.49726e11	−	8.64442e10i	0.630776	−	0.364178i
$699$		0			0
$700$	1.53405e11	+	6.19641e10i	0.638922	+	0.258076i
$701$			5.97428e10i			0.247408i	0.992319	+	0.123704i	$0.0394773\pi$
$701$			5.97428e10i			0.247408i	−0.992319	+	0.123704i	$0.960523\pi$
$702$		0			0
$703$	2.19809e11	−	3.80721e11i	0.899963	−	1.55878i
$704$	−3.24306e10	−	1.87238e10i	−0.132027	−	0.0762260i
$705$		0			0
$706$	−3.24356e9			−0.0130558
$707$	1.70664e10	−	2.40005e9i	0.0683069	−	0.00960600i
$708$		0			0
$709$	−9.88523e10	−	1.71217e11i	−0.391203	−	0.677583i	0.601406	−	0.798944i	$-0.294608\pi$
$709$	−9.88523e10	−	1.71217e11i	−0.391203	−	0.677583i	−0.992608	+	0.121361i	$0.961274\pi$
$710$	−1.38399e11	−	7.99047e10i	−0.544628	−	0.314441i
$711$		0			0
$712$	−3.72422e10	−	6.45053e10i	−0.144916	−	0.251001i
$713$		−	7.69720e8i		−	0.00297834i
$714$		0			0
$715$	−8.59141e11			−3.28731
$716$	−9.48021e10	+	5.47340e10i	−0.360717	+	0.208260i
$717$		0			0
$718$	−4.16998e10	+	7.22261e10i	−0.156905	+	0.271767i
$719$	2.54198e11	−	1.46761e11i	0.951167	−	0.549157i	0.0577239	−	0.998333i	$-0.481616\pi$
$719$	2.54198e11	−	1.46761e11i	0.951167	−	0.549157i	0.893443	+	0.449176i	$0.148282\pi$
$720$		0			0
$721$	−1.25354e11	−	5.06337e10i	−0.463872	−	0.187369i
$722$		−	7.12655e10i		−	0.262259i
$723$		0			0
$724$	1.03229e10	−	1.78797e10i	0.0375704	−	0.0650739i
$725$	2.34099e10	+	1.35157e10i	0.0847320	+	0.0489201i
$726$		0			0
$727$	−3.36267e11			−1.20378			−0.601890	−	0.798579i	$-0.705585\pi$
$727$	−3.36267e11			−1.20378			−0.601890	+	0.798579i	$0.705585\pi$
$728$	−1.06873e11	−	1.36767e11i	−0.380490	−	0.486917i
$729$		0			0
$730$	1.36415e11	+	2.36277e11i	0.480364	+	0.832014i
$731$	2.40525e10	+	1.38867e10i	0.0842348	+	0.0486330i
$732$		0			0
$733$	−6.06222e9	−	1.05001e10i	−0.0209998	−	0.0363728i	0.855335	−	0.518076i	$-0.173352\pi$
$733$	−6.06222e9	−	1.05001e10i	−0.0209998	−	0.0363728i	−0.876334	+	0.481703i	$0.840018\pi$
$734$			4.74937e10i			0.163626i
$735$		0			0
$736$	8.93645e8			0.00304547
$737$	−4.35919e11	+	2.51678e11i	−1.47753	+	0.853051i
$738$		0			0
$739$	−1.31349e11	+	2.27503e11i	−0.440402	+	0.762798i	−0.997719	−	0.0675015i	$-0.978497\pi$
$739$	−1.31349e11	+	2.27503e11i	−0.440402	+	0.762798i	0.557318	+	0.830299i	$0.311831\pi$
$740$	−3.07822e11	+	1.77721e11i	−1.02653	+	0.592670i
$741$		0			0
$742$	2.39398e11	−	1.87072e11i	0.789778	−	0.617153i
$743$			4.31104e11i			1.41458i	0.706925	+	0.707289i	$0.250082\pi$
$743$			4.31104e11i			1.41458i	−0.706925	+	0.707289i	$0.749918\pi$
$744$		0			0
$745$	1.68659e11	−	2.92126e11i	0.547501	−	0.948299i
$746$	−1.62977e11	−	9.40950e10i	−0.526226	−	0.303816i
$747$		0			0
$748$	2.71097e11			0.866000
$749$	1.26405e11	−	3.12943e11i	0.401642	−	0.994348i
$750$		0			0
$751$	−1.31517e11	−	2.27794e11i	−0.413449	−	0.716114i	0.581816	−	0.813321i	$-0.302343\pi$
$751$	−1.31517e11	−	2.27794e11i	−0.413449	−	0.716114i	−0.995264	+	0.0972067i	$0.969009\pi$
$752$	3.87452e10	+	2.23695e10i	0.121156	+	0.0699496i
$753$		0			0
$754$	−1.41794e10	−	2.45595e10i	−0.0438705	−	0.0759860i
$755$		−	2.35111e11i		−	0.723579i
$756$		0			0
$757$	4.09969e11			1.24844			0.624220	−	0.781249i	$-0.285417\pi$
$757$	4.09969e11			1.24844			0.624220	+	0.781249i	$0.285417\pi$
$758$	1.49929e11	−	8.65613e10i	0.454158	−	0.262208i
$759$		0			0
$760$	−1.06488e11	+	1.84442e11i	−0.319188	+	0.552849i
$761$	4.00771e11	−	2.31385e11i	1.19497	−	0.689918i	0.235543	−	0.971864i	$-0.424313\pi$
$761$	4.00771e11	−	2.31385e11i	1.19497	−	0.689918i	0.959430	+	0.281946i	$0.0909799\pi$
$762$		0			0
$763$	4.04562e10	+	2.87679e11i	0.119368	+	0.848808i
$764$			2.55193e11i			0.749023i
$765$		0			0
$766$	−2.10973e11	+	3.65416e11i	−0.612790	+	1.06138i
$767$	8.09285e11	+	4.67241e11i	2.33841	+	1.35008i
$768$		0			0
$769$	−1.11444e10			−0.0318679			−0.0159339	−	0.999873i	$-0.505072\pi$
$769$	−1.11444e10			−0.0318679			−0.0159339	+	0.999873i	$0.505072\pi$
$770$	−1.75094e11	+	4.33483e11i	−0.498092	+	1.23313i
$771$		0			0
$772$	9.87927e10	+	1.71114e11i	0.278135	+	0.481744i
$773$	3.38397e11	+	1.95373e11i	0.947782	+	0.547202i	0.892391	−	0.451263i	$-0.149026\pi$
$773$	3.38397e11	+	1.95373e11i	0.947782	+	0.547202i	0.0553905	+	0.998465i	$0.482360\pi$
$774$		0			0
$775$	−4.29753e10	−	7.44355e10i	−0.119128	−	0.206335i
$776$			2.21234e11i			0.610105i
$777$		0			0
$778$	3.03876e10			0.0829427
$779$	5.32415e11	−	3.07390e11i	1.44577	−	0.834718i
$780$		0			0
$781$	1.30846e11	−	2.26633e11i	0.351688	−	0.609141i
$782$	−5.60269e9	+	3.23471e9i	−0.0149820	+	0.00864985i
$783$		0			0
$784$	−9.07871e10	+	2.60500e10i	−0.240303	+	0.0689513i
$785$			5.32676e11i			1.40276i
$786$		0			0
$787$	3.80501e11	−	6.59047e11i	0.991874	−	1.71798i	0.385759	−	0.922599i	$-0.373939\pi$
$787$	3.80501e11	−	6.59047e11i	0.991874	−	1.71798i	0.606115	−	0.795377i	$-0.292727\pi$
$788$	5.04665e10	+	2.91369e10i	0.130888	+	0.0755680i
$789$		0			0
$790$	−3.17150e11			−0.814246
$791$	2.20007e11	+	2.81545e11i	0.561992	+	0.719188i
$792$		0			0
$793$	−5.34962e11	−	9.26582e11i	−1.35279	−	2.34310i
$794$	1.14589e11	+	6.61581e10i	0.288311	+	0.166456i
$795$		0			0
$796$	−1.36731e10	−	2.36825e10i	−0.0340576	−	0.0589895i
$797$			2.99118e10i			0.0741326i	0.999313	+	0.0370663i	$0.0118013\pi$
$797$			2.99118e10i			0.0741326i	−0.999313	+	0.0370663i	$0.988199\pi$
$798$		0			0
$799$	−3.23883e11			−0.794695
$800$	8.64196e10	−	4.98944e10i	0.210985	−	0.121812i
$801$		0			0
$802$	−4.09932e10	+	7.10022e10i	−0.0990864	+	0.171623i
$803$	−3.86911e11	+	2.23383e11i	−0.930571	+	0.537265i
$804$		0			0
$805$	−1.55366e9	−	1.10479e10i	−0.00369976	−	0.0263085i
$806$			9.01714e10i			0.213663i
$807$		0			0
$808$	5.19742e9	−	9.00219e9i	0.0121939	−	0.0211204i
$809$	−8.59145e10	−	4.96028e10i	−0.200573	−	0.115801i	0.396350	−	0.918100i	$-0.370277\pi$
$809$	−8.59145e10	−	4.96028e10i	−0.200573	−	0.115801i	−0.596923	+	0.802299i	$0.703610\pi$
$810$		0			0
$811$	−6.75804e11			−1.56220			−0.781101	−	0.624405i	$-0.785342\pi$
$811$	−6.75804e11			−1.56220			−0.781101	+	0.624405i	$0.785342\pi$
$812$	−1.52814e10	+	2.14902e9i	−0.0351510	+	0.00494329i
$813$		0			0
$814$	−2.91024e11	−	5.04068e11i	−0.662874	−	1.14813i
$815$	−3.62897e11	−	2.09518e11i	−0.822531	−	0.474889i
$816$		0			0
$817$	−1.78647e10	−	3.09425e10i	−0.0400966	−	0.0694493i
$818$			3.72451e11i			0.831871i
$819$		0			0
$820$	−4.97065e11			−1.09941
$821$	−6.99792e11	+	4.04025e11i	−1.54027	+	0.889274i	−0.541446	+	0.840736i	$0.682123\pi$
$821$	−6.99792e11	+	4.04025e11i	−1.54027	+	0.889274i	−0.998821	+	0.0485382i	$0.984544\pi$
$822$		0			0
$823$	2.98474e9	−	5.16973e9i	0.00650590	−	0.0112686i	−0.862754	−	0.505624i	$-0.831262\pi$
$823$	2.98474e9	−	5.16973e9i	0.00650590	−	0.0112686i	0.869260	+	0.494355i	$0.164596\pi$
$824$	−7.06173e10	+	4.07709e10i	−0.153180	+	0.0884386i
$825$		0			0
$826$	4.00682e11	−	3.13103e11i	0.860755	−	0.672617i
$827$		−	2.59203e11i		−	0.554137i	−0.960850	−	0.277069i	$-0.910637\pi$
$827$		−	2.59203e11i		−	0.554137i	0.960850	−	0.277069i	$-0.0893630\pi$
$828$		0			0
$829$	−2.72059e11	+	4.71221e11i	−0.576031	+	0.997715i	0.419898	+	0.907571i	$0.362066\pi$
$829$	−2.72059e11	+	4.71221e11i	−0.576031	+	0.997715i	−0.995929	+	0.0901433i	$0.971267\pi$
$830$	1.85475e11	+	1.07084e11i	0.390816	+	0.225638i
$831$		0			0
$832$	−1.04689e11			−0.218478
$833$	4.74895e11	−	4.91940e11i	0.986319	−	1.02172i
$834$		0			0
$835$	7.42422e11	+	1.28591e12i	1.52723	+	2.64524i
$836$	−3.02030e11	−	1.74377e11i	−0.618337	−	0.356997i
$837$		0			0
$838$	−1.75044e11	−	3.03185e11i	−0.354953	−	0.614797i
$839$		−	1.59999e11i		−	0.322900i	−0.986881	−	0.161450i	$-0.948383\pi$
$839$		−	1.59999e11i		−	0.322900i	0.986881	−	0.161450i	$-0.0516171\pi$
$840$		0			0
$841$	4.97725e11			0.994960
$842$	2.89864e11	−	1.67353e11i	0.576694	−	0.332954i
$843$		0			0
$844$	1.46616e11	−	2.53946e11i	0.288943	−	0.500463i
$845$	−1.39915e12	+	8.07801e11i	−2.74434	+	1.58445i
$846$		0			0
$847$	−2.32625e11	−	9.39629e10i	−0.451984	−	0.182567i
$848$		−	1.83249e11i		−	0.354371i
$849$		0			0
$850$	−3.61204e11	+	6.25623e11i	−0.691953	+	1.19850i
$851$	1.20290e10	+	6.94496e9i	0.0229357	+	0.0132419i
$852$		0			0
$853$	−7.21121e11			−1.36211			−0.681055	−	0.732232i	$-0.738478\pi$
$853$	−7.21121e11			−1.36211			−0.681055	+	0.732232i	$0.738478\pi$
$854$	−5.76537e11	+	8.10783e10i	−1.08392	+	0.152431i
$855$		0			0
$856$	−1.01783e11	−	1.76294e11i	−0.189575	−	0.328354i
$857$	1.34969e9	+	7.79242e8i	0.00250213	+	0.00144460i	0.501251	−	0.865302i	$-0.332874\pi$
$857$	1.34969e9	+	7.79242e8i	0.00250213	+	0.00144460i	−0.498748	+	0.866747i	$0.666207\pi$
$858$		0			0
$859$	7.39522e10	+	1.28089e11i	0.135825	+	0.235255i	0.925912	−	0.377739i	$-0.123298\pi$
$859$	7.39522e10	+	1.28089e11i	0.135825	+	0.235255i	−0.790088	+	0.612994i	$0.789965\pi$
$860$			2.88881e10i			0.0528111i
$861$		0			0
$862$	5.60787e11			1.01571
$863$	6.27148e11	−	3.62084e11i	1.13065	−	0.652779i	0.186549	−	0.982446i	$-0.440270\pi$
$863$	6.27148e11	−	3.62084e11i	1.13065	−	0.652779i	0.944097	+	0.329667i	$0.106936\pi$
$864$		0			0
$865$	1.71503e11	−	2.97052e11i	0.306343	−	0.530602i
$866$	−9.83791e9	+	5.67992e9i	−0.0174917	+	0.0100988i
$867$		0			0
$868$	4.54963e10	+	1.83771e10i	0.0801488	+	0.0323741i
$869$		−	5.19342e11i		−	0.910698i
$870$		0			0
$871$	−7.03594e11	+	1.21866e12i	−1.22250	+	2.11744i
$872$	1.51745e11	+	8.76099e10i	0.262451	+	0.151526i
$873$		0			0
$874$	8.32263e9			0.0142631
$875$	−2.10478e11	−	2.69351e11i	−0.359066	−	0.459501i
$876$		0			0
$877$	−2.56322e11	−	4.43962e11i	−0.433299	−	0.750495i	0.563857	−	0.825873i	$-0.309317\pi$
$877$	−2.56322e11	−	4.43962e11i	−0.433299	−	0.750495i	−0.997155	+	0.0753777i	$0.975984\pi$
$878$	−2.12575e11	−	1.22730e11i	−0.357713	−	0.206526i
$879$		0			0
$880$	1.40988e11	+	2.44199e11i	0.235100	+	0.407205i
$881$		−	2.45126e11i		−	0.406897i	−0.979086	−	0.203449i	$-0.934785\pi$
$881$		−	2.45126e11i		−	0.406897i	0.979086	−	0.203449i	$-0.0652150\pi$
$882$		0			0
$883$	−7.48726e11			−1.23163			−0.615815	−	0.787891i	$-0.711173\pi$
$883$	−7.48726e11			−1.23163			−0.615815	+	0.787891i	$0.711173\pi$
$884$	6.56345e11	−	3.78941e11i	1.07479	−	0.620530i
$885$		0			0
$886$	−1.62810e11	+	2.81995e11i	−0.264208	+	0.457621i
$887$	5.46564e11	−	3.15559e11i	0.882970	−	0.509783i	0.0113338	−	0.999936i	$-0.496392\pi$
$887$	5.46564e11	−	3.15559e11i	0.882970	−	0.509783i	0.871637	+	0.490153i	$0.163059\pi$
$888$		0			0
$889$	8.38971e11	−	6.55594e11i	1.34320	−	1.04961i
$890$			5.60860e11i			0.893912i
$891$		0			0
$892$	−4.11397e10	+	7.12560e10i	−0.0649833	+	0.112554i
$893$	3.60839e11	+	2.08330e11i	0.567424	+	0.327602i
$894$		0			0
$895$	8.24285e11			1.28465
$896$	−2.13358e10	+	5.28212e10i	−0.0331037	+	0.0819551i
$897$		0			0
$898$	−1.39260e11	−	2.41206e11i	−0.214152	−	0.370922i
$899$	6.94282e9	+	4.00844e9i	0.0106291	+	0.00613672i
$900$		0			0
$901$	6.63303e11	+	1.14887e12i	1.00650	+	1.74330i
$902$		−	8.13959e11i		−	1.22964i
$903$		0			0
$904$	2.15511e11			0.322697
$905$	−1.34633e11	+	7.77302e10i	−0.200704	+	0.115877i
$906$		0			0
$907$	5.85765e11	−	1.01457e12i	0.865554	−	1.49918i	−0.000942990	−	1.00000i	$-0.500300\pi$
$907$	5.85765e11	−	1.01457e12i	0.865554	−	1.49918i	0.866497	−	0.499183i	$-0.166367\pi$
$908$	−8.21890e10	+	4.74519e10i	−0.120912	+	0.0698087i
$909$		0			0
$910$	1.82009e11	+	1.29424e12i	0.265416	+	1.88734i
$911$			1.03419e12i			1.50150i	0.660584	+	0.750752i	$0.270309\pi$
$911$			1.03419e12i			1.50150i	−0.660584	+	0.750752i	$0.729691\pi$
$912$		0			0
$913$	−1.75353e11	+	3.03720e11i	−0.252365	+	0.437110i
$914$	−5.32360e11	−	3.07358e11i	−0.762818	−	0.440413i
$915$		0			0
$916$	4.18109e11			0.593893
$917$	2.57420e10	−	6.37298e10i	0.0364054	−	0.0901291i
$918$		0			0
$919$	−4.06482e11	−	7.04048e11i	−0.569875	−	0.987052i	−0.996578	−	0.0826603i	$-0.973658\pi$
$919$	−4.06482e11	−	7.04048e11i	−0.569875	−	0.987052i	0.426703	−	0.904392i	$-0.359675\pi$
$920$	−5.82754e9	−	3.36453e9i	−0.00813456	−	0.00469649i
$921$		0			0
$922$	−2.48540e11	−	4.30484e11i	−0.343932	−	0.595708i
$923$		−	7.31592e11i		−	1.00800i
$924$		0			0
$925$	1.55102e12			2.11860
$926$	6.34317e11	−	3.66223e11i	0.862705	−	0.498083i
$927$		0			0
$928$	−4.65380e9	+	8.06061e9i	−0.00627503	+	0.0108687i
$929$	−4.82350e11	+	2.78485e11i	−0.647589	+	0.373885i	−0.787532	−	0.616274i	$-0.788641\pi$
$929$	−4.82350e11	+	2.78485e11i	−0.647589	+	0.373885i	0.139943	+	0.990160i	$0.455308\pi$
$930$		0			0
$931$	−8.45512e11	+	2.42607e11i	−1.12544	+	0.322927i
$932$		−	1.90704e11i		−	0.252752i
$933$		0			0
$934$	3.01138e11	−	5.21587e11i	0.395711	−	0.685392i
$935$	−1.76785e12	−	1.02067e12i	−2.31312	−	1.33548i
$936$		0			0
$937$	−4.49572e10			−0.0583232			−0.0291616	−	0.999575i	$-0.509284\pi$
$937$	−4.49572e10			−0.0583232			−0.0291616	+	0.999575i	$0.509284\pi$
$938$	4.71486e11	+	6.03366e11i	0.609057	+	0.779417i
$939$		0			0
$940$	−1.68440e11	−	2.91747e11i	−0.215742	−	0.373676i
$941$	8.39253e11	+	4.84543e11i	1.07037	+	0.617979i	0.928283	−	0.371875i	$-0.121285\pi$
$941$	8.39253e11	+	4.84543e11i	1.07037	+	0.617979i	0.142089	+	0.989854i	$0.454618\pi$
$942$		0			0
$943$	9.71212e9	+	1.68219e10i	0.0122819	+	0.0212729i
$944$		−	3.06704e11i		−	0.386218i
$945$		0			0
$946$	−4.73051e10			−0.0590668
$947$	−5.89910e10	+	3.40585e10i	−0.0733476	+	0.0423472i	−0.536225	−	0.844075i	$-0.680150\pi$
$947$	−5.89910e10	+	3.40585e10i	−0.0733476	+	0.0423472i	0.462878	+	0.886422i	$0.346817\pi$
$948$		0			0
$949$	−6.24494e11	+	1.08165e12i	−0.769951	+	1.33359i
$950$	8.04837e11	−	4.64673e11i	0.988128	−	0.570496i
$951$		0			0
$952$	−5.74319e10	−	4.08390e11i	−0.0699206	−	0.497196i
$953$			1.52825e12i			1.85277i	0.376574	+	0.926387i	$0.377102\pi$
$953$			1.52825e12i			1.85277i	−0.376574	+	0.926387i	$0.622898\pi$
$954$		0			0
$955$	9.60790e11	−	1.66414e12i	1.15509	−	2.00067i
$956$	5.73363e11	+	3.31031e11i	0.686433	+	0.396312i
$957$		0			0
$958$	9.99175e11			1.18626
$959$	6.77945e11	−	9.53394e10i	0.801531	−	0.112719i
$960$		0			0
$961$	4.13700e11	+	7.16550e11i	0.485056	+	0.840142i
$962$	−1.40918e12	−	8.13591e11i	−1.64538	−	0.949961i
$963$		0			0
$964$	2.60505e11	+	4.51208e11i	0.301653	+	0.522479i
$965$		−	1.48780e12i		−	1.71568i
$966$		0			0
$967$	1.40559e12			1.60751			0.803754	−	0.594961i	$-0.202833\pi$
$967$	1.40559e12			1.60751			0.803754	+	0.594961i	$0.202833\pi$
$968$	−1.31047e11	+	7.56603e10i	−0.149254	+	0.0861721i
$969$		0			0
$970$	8.32936e11	−	1.44269e12i	0.940859	−	1.62962i
$971$	−1.01451e12	+	5.85728e11i	−1.14125	+	0.658899i	−0.946739	−	0.322002i	$-0.895644\pi$
$971$	−1.01451e12	+	5.85728e11i	−1.14125	+	0.658899i	−0.194507	+	0.980901i	$0.562311\pi$
$972$		0			0
$973$	−9.39557e11	+	7.34195e11i	−1.04827	+	0.819143i
$974$		−	1.09234e12i		−	1.21373i
$975$		0			0
$976$	−1.75579e11	+	3.04111e11i	−0.193496	+	0.335146i
$977$	2.22914e11	+	1.28700e11i	0.244658	+	0.141253i	0.617316	−	0.786715i	$-0.288220\pi$
$977$	2.22914e11	+	1.28700e11i	0.244658	+	0.141253i	−0.372658	+	0.927969i	$0.621553\pi$
$978$		0			0
$979$	−9.18425e11			−0.999800
$980$	6.90108e11	+	1.71935e11i	0.748191	+	0.186406i
$981$		0			0
$982$	−3.95216e11	−	6.84534e11i	−0.425000	−	0.736121i
$983$	−3.88115e11	−	2.24078e11i	−0.415667	−	0.239986i	0.277555	−	0.960710i	$-0.410476\pi$
$983$	−3.88115e11	−	2.24078e11i	−0.415667	−	0.239986i	−0.693222	+	0.720724i	$0.743809\pi$
$984$		0			0
$985$	−2.19398e11	−	3.80008e11i	−0.233071	−	0.403690i
$986$		−	6.73811e10i		−	0.0712903i
$987$		0			0
$988$	−9.74982e11			−1.02322
$989$	9.77643e8	−	5.64442e8i	0.00102187	−	0.000589976i
$990$		0			0
$991$	1.29796e11	−	2.24813e11i	0.134575	−	0.233091i	−0.790860	−	0.611997i	$-0.790366\pi$
$991$	1.29796e11	−	2.24813e11i	0.134575	−	0.233091i	0.925435	+	0.378906i	$0.123700\pi$
$992$	2.56300e10	−	1.47975e10i	0.0264668	−	0.0152806i
$993$		0			0
$994$	−3.69127e11	−	1.49100e11i	−0.378121	−	0.152732i
$995$			2.05914e11i			0.210084i
$996$		0			0
$997$	−7.82185e11	+	1.35478e12i	−0.791642	+	1.37116i	0.133307	+	0.991075i	$0.457440\pi$
$997$	−7.82185e11	+	1.35478e12i	−0.791642	+	1.37116i	−0.924950	+	0.380090i	$0.875893\pi$
$998$	7.86086e11	+	4.53847e11i	0.792407	+	0.457496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.s.a.53.1	✓	20
3.2	odd	2	inner	126.9.s.a.53.10	yes	20
7.2	even	3	inner	126.9.s.a.107.10	yes	20
21.2	odd	6	inner	126.9.s.a.107.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.s.a.53.1	✓	20	1.1	even	1	trivial
126.9.s.a.53.10	yes	20	3.2	odd	2	inner
126.9.s.a.107.1	yes	20	21.2	odd	6	inner
126.9.s.a.107.10	yes	20	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-834.700 + 481.914i) q^{5} +(-1891.88 + 1478.37i) q^{7} +1448.15i q^{8} +O(q^{10})\)	\(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-834.700 + 481.914i) q^{5} +(-1891.88 + 1478.37i) q^{7} +1448.15i q^{8} +(5452.24 - 9443.55i) q^{10} +(15464.1 + 8928.20i) q^{11} +49919.6 q^{13} +(10173.7 - 25187.1i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(102719. + 59304.9i) q^{17} +(-76293.2 - 132144. i) q^{19} +123370. i q^{20} -202022. q^{22} +(4175.14 - 2410.52i) q^{23} +(269170. - 466216. i) q^{25} +(-489110. + 282388. i) q^{26} +(42798.4 + 304333. i) q^{28} +50212.6i q^{29} +(79829.4 - 138269. i) q^{31} +(160530. + 92681.9i) q^{32} -1.34192e6 q^{34} +(866709. - 2.14572e6i) q^{35} +(1.44056e6 + 2.49512e6i) q^{37} +(1.49503e6 + 863159. i) q^{38} +(-697886. - 1.20877e6i) q^{40} +4.02906e6i q^{41} +234158. q^{43} +(1.97940e6 - 1.14281e6i) q^{44} +(-27271.9 + 47236.3i) q^{46} +(-2.36482e6 + 1.36533e6i) q^{47} +(1.39365e6 - 5.59381e6i) q^{49} +6.09062e6i q^{50} +(3.19485e6 - 5.53365e6i) q^{52} +(9.68616e6 + 5.59231e6i) q^{53} -1.72105e7 q^{55} +(-2.14091e6 - 2.73974e6i) q^{56} +(-284045. - 491981. i) q^{58} +(1.62118e7 + 9.35988e6i) q^{59} +(-1.07165e7 - 1.85615e7i) q^{61} +1.80633e6i q^{62} -2.09715e6 q^{64} +(-4.16679e7 + 2.40569e7i) q^{65} +(-1.40946e7 + 2.44125e7i) q^{67} +(1.31480e7 - 7.59103e6i) q^{68} +(3.64604e6 + 2.59265e7i) q^{70} -1.46554e7i q^{71} +(-1.25100e7 + 2.16679e7i) q^{73} +(-2.82290e7 - 1.62980e7i) q^{74} -1.95311e7 q^{76} +(-4.24554e7 + 5.97051e6i) q^{77} +(-1.45422e7 - 2.51878e7i) q^{79} +(1.36757e7 + 7.89568e6i) q^{80} +(-2.27918e7 - 3.94766e7i) q^{82} +1.96403e7i q^{83} -1.14319e8 q^{85} +(-2.29427e6 + 1.32460e6i) q^{86} +(-1.29294e7 + 2.23944e7i) q^{88} +(-4.45431e7 + 2.57170e7i) q^{89} +(-9.44421e7 + 7.37995e7i) q^{91} -617092. i q^{92} +(1.54469e7 - 2.67548e7i) q^{94} +(1.27364e8 + 7.35335e7i) q^{95} +1.52770e8 q^{97} +(1.79884e7 + 6.26916e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) \) 20 * q + 1280 * q^4 - 3710 * q^7	\( 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) \) 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more